Loren Booda
Aug17-03, 02:46 AM
Construct a plane containing N points, no three of which are collinear. Calculate the n distinct ways they can be connected exhaustively (a Traveling Salesman problem).
Next, find the number m of all possible line segments bounded by the N points and/or by any points of intersection between their N(N-1)/2 interconnections. (For a set of N=4 points, m=10; for N=5, m=35.)
As N-->[oo], which approaches infinity more rapidly, n or m?
Next, find the number m of all possible line segments bounded by the N points and/or by any points of intersection between their N(N-1)/2 interconnections. (For a set of N=4 points, m=10; for N=5, m=35.)
As N-->[oo], which approaches infinity more rapidly, n or m?